We propose an algorithm for an optimal adaptive selection of points from the design domain of input random variables that are needed for an accurate estimation of failure probability and the determination of the boundary between safe and failure domains. The method is particularly useful when each evaluation of the performance function g(x) is very expensive and the function can be characterized as either highly nonlinear, noisy, or even discrete-state (e.g., binary). In such cases, only a limited number of calls is feasible, and gradients of g(x) cannot be used. The input design domain is progressively segmented by expanding and adaptively refining mesh-like lock-free geometrical structure. The proposed triangulation-based approach effectively combines the features of simulation and approximation methods. The algorithm performs two independent tasks: (i) the estimation of probabilities through an ingenious combination of deterministic cubature rules and the application of the divergence theorem and (ii) the sequential extension of the experimental design with new points. The sequential selection of points from the design domain for future evaluation of g(x) is carried out through a new learning function, which maximizes instantaneous information gain in terms of the probability classification that corresponds to the local region. The extension may be halted at any time, e.g., when sufficiently accurate estimations are obtained. Due to the use of the exact geometric representation in the input domain, the algorithm is most effective for problems of a low dimension, not exceeding eight. The method can handle random vectors with correlated non-Gaussian marginals. The estimation accuracy can be improved by employing a smooth surrogate model. Finally, we define new factors of global sensitivity to failure based on the entire failure surface weighted by the density of the input random vector.
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In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a Bayesian inference framework. However in many practical problems, only data at the aggregate level is available and as a result the likelihood function is not available, which poses challenge for Bayesian methods. In particular, we consider the situation where the distributions of the particles are observed. We propose a Wasserstein distance based sequential Monte Carlo sampler to solve the problem: the Wasserstein distance is used to measure the similarity between the observed and the simulated particle distributions and the sequential Monte Carlo samplers is used to deal with the sequentially available observations. Two real-world examples are provided to demonstrate the performance of the proposed method.
Domination problems in general can capture situations in which some entities have an effect on other entities (and sometimes on themselves). The usual goal is to select a minimum number of entities that can influence a target group of entities or to influence a maximum number of target entities with a certain number of available influencers. In this work, we focus on the distinction between \textit{internal} and \textit{external} domination in the respective maximization problem. In particular, a dominator can dominate its entire neighborhood in a graph, internally dominating itself, while those of its neighbors which are not dominators themselves are externally dominated. We study the problem of maximizing the external domination that a given number of dominators can yield and we present a 0.5307-approximation algorithm for this problem. Moreover, our methods provide a framework for approximating a number of problems that can be cast in terms of external domination. In particular, we observe that an interesting interpretation of the maximum coverage problem can capture a new problem in elections, in which we want to maximize the number of \textit{externally represented} voters. We study this problem in two different settings, namely Non-Secrecy and Rational-Candidate, and provide approximability analysis for two alternative approaches; our analysis reveals, among other contributions, that an earlier resource allocation algorithm is, in fact, a 0.462-approximation algorithm for maximum external domination in directed graphs.
Proactive failure detection of instances is vitally essential to microservice systems because an instance failure can propagate to the whole system and degrade the system's performance. Over the years, many single-modal (i.e., metrics, logs, or traces) data-based nomaly detection methods have been proposed. However, they tend to miss a large number of failures and generate numerous false alarms because they ignore the correlation of multimodal data. In this work, we propose AnoFusion, an unsupervised failure detection approach, to proactively detect instance failures through multimodal data for microservice systems. It applies a Graph Transformer Network (GTN) to learn the correlation of the heterogeneous multimodal data and integrates a Graph Attention Network (GAT) with Gated Recurrent Unit (GRU) to address the challenges introduced by dynamically changing multimodal data. We evaluate the performance of AnoFusion through two datasets, demonstrating that it achieves the F1-score of 0.857 and 0.922, respectively, outperforming the state-of-the-art failure detection approaches.
Light field (LF) cameras record both intensity and directions of light rays, and encode 3D scenes into 4D LF images. Recently, many convolutional neural networks (CNNs) have been proposed for various LF image processing tasks. However, it is challenging for CNNs to effectively process LF images since the spatial and angular information are highly inter-twined with varying disparities. In this paper, we propose a generic mechanism to disentangle these coupled information for LF image processing. Specifically, we first design a class of domain-specific convolutions to disentangle LFs from different dimensions, and then leverage these disentangled features by designing task-specific modules. Our disentangling mechanism can well incorporate the LF structure prior and effectively handle 4D LF data. Based on the proposed mechanism, we develop three networks (i.e., DistgSSR, DistgASR and DistgDisp) for spatial super-resolution, angular super-resolution and disparity estimation. Experimental results show that our networks achieve state-of-the-art performance on all these three tasks, which demonstrates the effectiveness, efficiency, and generality of our disentangling mechanism. Project page: //yingqianwang.github.io/DistgLF/.
Regression analysis under the assumption of monotonicity is a well-studied statistical problem and has been used in a wide range of applications. However, there remains a lack of a broadly applicable methodology that permits information borrowing, for efficiency gains, when jointly estimating multiple monotonic regression functions. We introduce such a methodology by extending the isotonic regression problem presented in the article "The isotonic regression problem and its dual" (Barlow and Brunk, 1972). The presented approach can be applied to both fixed and random designs and any number of explanatory variables (regressors). Our framework penalizes pairwise differences in the values (levels) of the monotonic function estimates, with the weight of penalty being determined based on a statistical test, which results in information being shared across data sets if similarities in the regression functions exist. Function estimates are subsequently derived using an iterative optimization routine that uses existing solution algorithms for the isotonic regression problem. Simulation studies for normally and binomially distributed response data illustrate that function estimates are consistently improved if similarities between functions exist, and are not oversmoothed otherwise. We further apply our methodology to analyse two public health data sets: neonatal mortality data for Porto Alegre, Brazil, and stroke patient data for North West England.
The branch-and-bound algorithm based on decision diagrams introduced by Bergman et al. in 2016 is a framework for solving discrete optimization problems with a dynamic programming formulation. It works by compiling a series of bounded-width decision diagrams that can provide lower and upper bounds for any given subproblem. Eventually, every part of the search space will be either explored or pruned by the algorithm, thus proving optimality. This paper presents new ingredients to speed up the search by exploiting the structure of dynamic programming models. The key idea is to prevent the repeated exploration of nodes corresponding to the same dynamic programming states by storing and querying thresholds in a data structure called the Barrier. These thresholds are based on dominance relations between partial solutions previously found. They can be further strengthened by integrating the filtering techniques introduced by Gillard et al. in 2021. Computational experiments show that the pruning brought by the Barrier allows to significantly reduce the number of nodes expanded by the algorithm. This results in more benchmark instances of difficult optimization problems being solved in less time while using narrower decision diagrams.
Out-of-distribution (OOD) detection is a critical requirement for the deployment of deep neural networks. This paper introduces the HEAT model, a new post-hoc OOD detection method estimating the density of in-distribution (ID) samples using hybrid energy-based models (EBM) in the feature space of a pre-trained backbone. HEAT complements prior density estimators of the ID density, e.g. parametric models like the Gaussian Mixture Model (GMM), to provide an accurate yet robust density estimation. A second contribution is to leverage the EBM framework to provide a unified density estimation and to compose several energy terms. Extensive experiments demonstrate the significance of the two contributions. HEAT sets new state-of-the-art OOD detection results on the CIFAR-10 / CIFAR-100 benchmark as well as on the large-scale Imagenet benchmark. The code is available at: //github.com/MarcLafon/heat_ood.
Neural demyelination and brain damage accumulated in white matter appear as hyperintense areas on T2-weighted MRI scans in the form of lesions. Modeling binary images at the population level, where each voxel represents the existence of a lesion, plays an important role in understanding aging and inflammatory diseases. We propose a scalable hierarchical Bayesian spatial model, called BLESS, capable of handling binary responses by placing continuous spike-and-slab mixture priors on spatially-varying parameters and enforcing spatial dependency on the parameter dictating the amount of sparsity within the probability of inclusion. The use of mean-field variational inference with dynamic posterior exploration, which is an annealing-like strategy that improves optimization, allows our method to scale to large sample sizes. Our method also accounts for underestimation of posterior variance due to variational inference by providing an approximate posterior sampling approach based on Bayesian bootstrap ideas and spike-and-slab priors with random shrinkage targets. Besides accurate uncertainty quantification, this approach is capable of producing novel cluster size based imaging statistics, such as credible intervals of cluster size, and measures of reliability of cluster occurrence. Lastly, we validate our results via simulation studies and an application to the UK Biobank, a large-scale lesion mapping study with a sample size of 40,000 subjects.
Unsupervised domain adaptation has recently emerged as an effective paradigm for generalizing deep neural networks to new target domains. However, there is still enormous potential to be tapped to reach the fully supervised performance. In this paper, we present a novel active learning strategy to assist knowledge transfer in the target domain, dubbed active domain adaptation. We start from an observation that energy-based models exhibit free energy biases when training (source) and test (target) data come from different distributions. Inspired by this inherent mechanism, we empirically reveal that a simple yet efficient energy-based sampling strategy sheds light on selecting the most valuable target samples than existing approaches requiring particular architectures or computation of the distances. Our algorithm, Energy-based Active Domain Adaptation (EADA), queries groups of targe data that incorporate both domain characteristic and instance uncertainty into every selection round. Meanwhile, by aligning the free energy of target data compact around the source domain via a regularization term, domain gap can be implicitly diminished. Through extensive experiments, we show that EADA surpasses state-of-the-art methods on well-known challenging benchmarks with substantial improvements, making it a useful option in the open world. Code is available at //github.com/BIT-DA/EADA.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
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